Answer the following question. Round your answers to the nearest cent if necessary
Rickey Smith is an engineer. His annual salary is $85,425.00 per year. What is his monthly salary?
O A. $7,118.75
O B. $6,966.50
O C. $1,642.79
OD. $1,708.50

Answer:

\(f^{-1}(x)=\frac{1}{6}\ln(x+9)\)

Step-by-step explanation:

So we have the function:

\(f(x)=e^{6x}-9\)

To solve for the inverse of a function, change f(x) and x, change the f(x) to f⁻¹(x), and solve for it. Therefore:

\(x=e^{6f^{-1}(x)}-9\)

Add 9 to both sides:

\(x+9=e^{6f^{-1}(x)}\)

Take the natural log of both sides:

\(\ln(x+9)=\ln(e^{6f^{-1}(x)})\)

The right side cancels:

\(\ln(x+9)=6f^{-1}(x)\)

Divide both sides by 6:

\(f^{-1}(x)=\frac{1}{6}\ln(x+9)\)

And we're done!

Answer:

d: x = -8

Step-by-step explanation:

40 + 65 + x + 83 = 180  (sum of internal angles of a triangle)

x = 180 - 40 - 65 - 83

x = -8

Answer:

- Discount car rentals charges less daily

- After 3 days

Step-by-step explanation:

Required

Which charges less per day

When is the total cost the same

First, calculate the slope (m)

\(m = \frac{y_2 - y_1}{x_2 - x_1}\)

From the table, we have:

\((x_1,y_1) = (2,185)\)

\((x_2,y_2) = (6,345)\)

So, we have:

\(m = \frac{345 - 185}{6 - 2}\)

\(m = \frac{160}{4}\)

\(m = 40\)

The equation is then calculated as:

\(y = m(x - x_1) + y_1\)

\(y = 40(x - 2) + 185\)

\(y = 40x - 80 + 185\)

\(y = 40x + 105\)

So, the equation of the table (i.e. Discount Car rental) is: \(y = 40x + 105\)

While the equation of Pay Less is: \(y = 55x + 60\)

The company that charges less per day has the smaller slope and that is: Discount car rental because the slope (40) is less than the slope (55)

For the total cost to be the same, we simply equate both expressions:

i.e.

\(y = y\)

\(55x + 60 = 40x + 105\)

\(55x - 40x = - 60 + 105\)

\(15x =45\)

\(x = 3\)

Answer:

∠ x = 58°

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠  BAD is an exterior angle of the triangle , then

x + 56° = 114° ( subtract 56° from both sides )

x = 58°

Then, multiply this result by 100 to get the percentage. In this case, 120 is 80% of 150.

To use a double number line diagram to find what percent 120 is of 150, you need to create a diagram with two parallel lines. On the top line, mark 150 at one end and 100 at the other.

On the bottom line, mark 120 at one end and leave the other end blank. Then, draw diagonal lines connecting 120 on the bottom line to 150 on the top line and 100 on the top line to the blank end of the bottom line.

This creates two triangles. The height of the triangle with 120 is the percentage you're looking for.

To find this percentage, divide the length of the diagonal line connecting 120 and 150 by the length of the diagonal line connecting 100 and the blank end of the bottom line.

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From the given below solution the value of m EF is 25%.

A circle graph, also known as a pie chart, is a type of data visualization that displays data as a circular graph, divided into sectors that represent numerical proportions.

Each sector of the circle represents a percentage or proportion of the total data set, and the size of each sector is proportional to its corresponding value.

To find m EF, we need to add the percentages of participation in sports E and F:

m EF = percentage of participation in sports E + percentage of participation in sports F

m EF = 11% + 14%

m EF = 25%

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Answer:

Step-by-step explanation:

The reading game equation is 3x + 5. That means that every day the game is for sale he will make $3. The math game is parabolic and doesn't have a slope for which to make the same statement about the amount of money made per day. Where they intersect is where the revenue for each will be the same. On the x axis we have the number of days and on the y axis we have the number of dollars. Solving them algebraically:

\(2x^2+8x+2=3x+5\) and get everything on one side and set it equal to 0:

\(2x^2+5x-3=0\) and factor that however you have learned to factor that quadratic to get:

x = 1/2, -3

The x value indicates the number of days that it would take for the revenue for the games to be the same. Since time can never be negative, we discount the value of -3 and say that it would take 1/2 of a day for the revenue for the games to be the same. As far as the graph goes, I attached a pic below. The red line is the reading game graph and the blue line is the math game parabola. We only need the first quadrant when we graph something like this because, again, days can never be negative so quadrant 2 and 3 are out where x is negative; likewise, the number of dollars will never be negative either, so quadrants 3 and 4 are out. Where those 2 graphs intersect is the number of days that the revenues are the same.

a. Category with the greatest frequency is 20 - 24

b. 14 students

c. The percentage is 7%

Frequency is simply described as the number of times an event or observation happened in a given study or experiment that is carried out.

From the information given, we have that;

a. The category with the greatest frequency is the one with most words spelt, we have;

20 - 24

b. The number of students that spelt 35 - 39 words is traceable to

14 students

c. If the total number of students is 200

Then, the percent of students in the 35 - 39 category is;

14/200 × 100/1

Multiply the values

7%

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Answer:

5 oranges and 10 apples were sold  

Step-by-step explanation:

Let x be the number of oranges sold and y be the number of apples sold

Since 15 fruits were sold in all we get the following equation

x + y = 15 ....................[1]

Each orange costs $1 so if x oranges were sold that would fetch x dollars in sales = x dollars in sales

Each apple costs $2 so if y apples were sold, that would result in 2y dollars in sales

Total sales in $ = x + 2y and we know this is $25 so we get the second equation as

x + 2y = 25 ..................[2]

Look at the two equations. The coefficient of the x term is the same. We can eliminate the x term by subtracting equation [1] from equation [2] as follows:

x + 2y = 25
                    -
x  +   y = 15
-----------------
        y = 10

(2y - y = y and 25-15 = 10)

Now that we know y = 10, we can use equation [1] to find x

x + 10 = 15

which makes x = 5

ANSWER

5 oranges and 10 apples were sold  

Answer:

5.3%

Step-by-step explanation:

% Increase = Increase / Original Number × 100.

68/1283 * 100

= 5.3%

Irene has 49 Books, and Alejandro has 24 books.

Let's assume that Irene has x books, and Alejandro has y books. According to the given information, we can form the following equations:

1. Irene has twice as many books as Alejandro plus 1:

  x = 2y + 1

2. The total number of books between Irene and Alejandro is 73:

  x + y = 73

We can now solve this system of equations to find the values of x and y.

Substituting the value of x from equation (1) into equation (2), we have:

(2y + 1) + y = 73

3y + 1 = 73

3y = 72

y = 24

Now, we can substitute the value of y into equation (1) to find x:

x = 2(24) + 1

x = 49

Therefore, Irene has 49 books, and Alejandro has 24 books.

To verify our solution, we can check if the sum of their books equals 73:

49 + 24 = 7

So, our solution is correct.

In conclusion, Irene has 49 books, and Alejandro has 24 books.

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Answer:

Step-by-step explanation:

We know that the sides in a square are equal length. We also know that you have to multiply length by width to get area. So if we know that the length of one side is 16 feet then all we have to do if multiply 16 by 16. Hence why the answer is 256 square feet of carpet.

The original price of the camera is x = $ 324

Given data ,

Let the original price of the camera be x.

Iskandar sells the camera to Teck Meng at a profit of 15%, so he sells it for 1.15x.

Teck Meng then sells the camera to Ryan at a loss of 10%, which means he sells it for 0.9(414) = 372.60.

Since Teck Meng bought the camera for 1.15x and sold it for 372.60, we can set up the equation:

1.15x = 372.60

Divide by 1.15 on both sides , we get

x = 324

Hence , the original price of the camera was $ 324

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Answer: 2 x 9 = 18

Step-by-step explanation:

Multiplication is division’s inverse operation.

Answer: 2 rays that meet an endpoint

The value of x is -3 when value of y = 15 by using the property proportion as x and y are directly related to each other.

What is direct relation?

Two variables x and y are directly related to each other if x increases or decreases the value of y also increases or decreases proportionally.

We are given that value of y is -50 then value of x is 10

We have to find the value of x when y is 15

We solve it using proportion

we have,

10/x = -50/15

On separating the variable from the constant and then simplifying we get,

x=-3

Hence the value of x is -3 when y is 15

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The probability that either event A or B will occur is 43/60

Using the parameters given

n(A) = 29

n(B) = 14

Total number of events = 29+17+14 = 60

The probability of each event :

P(A) = 29/60

P(B) = 14/60

P(A or B ) = P(A) + P(B)

P(A or B ) = 29/60 + 14/60

P(A or B ) = 43/60

Therefore, the probability of A or B is 43/60

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5π/3=5π/3×180/π=300°

300° is the correct answer

Answer:

300 degrees

Step-by-step explanation:

To convert from radians to degrees, multiply by 180/ pi

5 pi /3  * 180/pi

5/3 * 180

5 * 60

300

Using the values of the table we can estimate the limit to be 1, so the correct option is the third one.

We want to take the limit of the difference quotient when h tends to zero.

Then we can use the table.

Let's say that h = 0.001 (really close to zero)

Then:

(f(3 + h) - f(3))/h = (f(3.001) - f(3))/0.001

Using the table, we can see that:

f(3.001) = 5.001

f(3) = 5

Then we will get:

(5.001 - 5)/0.001 = 1

Then the limit appears to be 1.

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Answer:

percent=25.56%

Step-by-step explanation:

Percentages

To know the percentage of having n elements out of a total of m elements, we calculate the ratio n/m and express the result as a percentage.

The shoe store has 23 pairs of white shoes out of 90 total pairs of shoes. The percent of white tennis shoes is calculated as follows:

\(\displaystyle percent= \frac{23}{90}*100\%\)

Operating:

percent=25.56%

The number of minutes spent higher than 38 meters above the ground on the Ferris wheel ride is approximately 1.0918 minutes.

To solve this problem, we need to determine the angular position of the Ferris wheel when it is 38 meters above the ground.

The Ferris wheel has a diameter of 50 meters, which means its radius is half of that, or 25 meters.

When the Ferris wheel is at its highest point, the radius and the height from the ground are aligned, forming a right triangle.

The height of this right triangle is the sum of the radius (25 meters) and the platform height (4 meters), which equals 29 meters.

To find the angle at which the Ferris wheel is 38 meters above the ground, we can use the inverse sine (arcsine) function.

The formula is:

θ = arcsin(h / r)

where θ is the angle in radians, h is the height above the ground (38 meters), and r is the radius of the Ferris wheel (25 meters).

θ = arcsin(38 / 29) ≈ 1.0918 radians

Now, we know the angle at which the Ferris wheel is 38 meters above the ground.

To calculate the time spent higher than 38 meters, we need to find the fraction of the total revolution that corresponds to this angle.

The Ferris wheel completes one full revolution in 2 minutes, which is equivalent to 2π radians.

Therefore, the fraction of the revolution corresponding to an angle of 1.0918 radians is:

Fraction = θ / (2π) ≈ 1.0918 / (2π)

Finally, we can calculate the time spent higher than 38 meters by multiplying the fraction of the revolution by the total time for one revolution:

Time = Fraction \(\times\) Total time per revolution = (1.0918 / (2π)) \(\times\) 2 minutes

Calculating this expression will give us the answer in minutes.

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The relative minimum point is B. Option B is the correct option.

What is the relative minimum?

The function's graph makes it simple to locate relative minima. It is the pivotal point in the function's graph. Relative minima are locations where the function's graph shifts from decreasing to increasing. A point that is lower than the points to its left and right is said to be at its relative minima.

The points of the graph function are A, B, C, D.

The lowest point among the given points on the graph is B.

Thus the relative minimum point is B.

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Answer:

1)

Angle 1: 59

Angle 2: 88

Angle 3: 147

2)x =21

Step-by-step explanation:

1)

Angle on a straight line add up to 180 degrees and angles in a triangle add to 180 degrees

2)

Opposite angles are equal. (4x) and (2x+42) are opposite therefore equal, so

4x=2x+42

Minus 2x from both sides

2x = 42

Find 1x by dividing 42 by 2, therefore

X=21

Answer:

A

Step-by-step explanation:

the answer is A because you can tell the line has a negative slope since its going from left to right rather than right to left and then you do rise/run so the rise=2 and the run=3 so the answer for slope would be -2/3

Answer:

-2/3

Step-by-step explanation:

First you need to find two exact points the use your formula. I used (0,1) and (-3,3).

y2-y1 / x2-x1

Or just use rise over run and count up 2 and across to the left 3 and also realize it's a negative slope going down from the left so your answer will be negative.

I hope I helped you. You can comment if you need anymore help.

Answer: ME

Step-by-step explanation:

Answer:

166

Step-by-step explanation:

Since the lines are parallel, A=B. 7x+40=3x+112, 4x=72, x=18. A=166

Answer:

y=4/5x1

Step-by-step explanation:

Answer:

g(f(-4)) = -8

f(g(x)) = 13-10x

Step-by-step explanation:

g(f(-4)):

Plug in the equation f(x) into the variable x of g(x), we have:

\((gof)= 5(7-2x)-3\)

Plug in x = -4 and the answer is -8

f(g(x)):
Plug in the equation g(x) into the variable x of f(x), we have:

\(7-2(5x-3) = 7-10x+6 = 13-10x\)

Answer:

Okie

Step-by-step explanation:

Answer:

yay thanks

Step-by-step explanation: